报告主题：多项式可积哈密顿系统与平面曲线的对称幂
报告人：Alexander V. Mikhailov 教授 （英国 University of Leeds）
报告时间：2019年4月15日（周一）13：30
报告地点：校本部G508
邀请人：张大军
报告摘要： We have found quite general construction of k commuting vector fields on k-th symmetric power of C^m and also of k commuting tangent vector fields to the k-th symmetric power of an a
ffine variety V which is a subset of C^m. Application of this construction to k-th symmetric power of a plane algebraic curve Vg of genus g leads to k integrable Hamiltonian systems on C^{2k} (or on R^{2k}, if the base field is R). In the case of a hyperelliptic curve Vg of genus g and k = g our system is equivalent to the well known Dubrovin system which has been derived and studied in the theory of finite gap solutions (algebra-geometric integration) of the Korteweg-de-Vrise equation. We have found the coordinates in which the systems obtained and their Hamiltonians are polynomial. For k = 2; 3 and g = 1; 2; 3 we present these systems explicitly as well as we discuss the problem of their integration.
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